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On the Asphericity of a Family of Positive Relative Group Presentations

Part of: Special aspects of infinite or finite groups Low-dimensional topology

Published online by Cambridge University Press:  05 January 2017

Suzana Aldwaik  and
Martin Edjvet
Suzana Aldwaik
Affiliation:
School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD, UK (martin.edjvet@nottingham.ac.uk)
Martin Edjvet
Affiliation:
School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD, UK (martin.edjvet@nottingham.ac.uk)
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Abstract

Excluding four exceptional cases, we determine the asphericity of the relative presentation for m ⩾ 2. If H = ⟨g, h⟩ ⩽ G, then the exceptional cases occur when H is isomorphic to C5 or C6.

Keywords

relative group presentationspicturesasphericity

MSC classification

Secondary: 20F05: Generators, relations, and presentations 57M05: Fundamental group, presentations, free differential calculus
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 60 , Issue 3 , August 2017 , pp. 545 - 564
Copyright
Copyright © Edinburgh Mathematical Society 2017 

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